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An Extension of the Dirichlet Density for Sets of Gaussian Integers

Published online by Cambridge University Press:  20 November 2018

L. C. Rêgo  and
R. J. Cintra
L. C. Rêgo
Affiliation:
Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540, Recife, PE, Brazil e-mail: [email protected]@stat.ufpe.org
R. J. Cintra
Affiliation:
Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540, Recife, PE, Brazil e-mail: [email protected]@stat.ufpe.org
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Abstract

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Several measures for the density of sets of integers have been proposed, such as the asymptotic density, the Schnirelmann density, and the Dirichlet density. There has been some work in the literature on extending some of these concepts of density to higher dimensional sets of integers. In this work, we propose an extension of the Dirichlet density for sets of Gaussian integers and investigate some of its properties.

Keywords

11B0511M9911N99Gaussian integersDirichlet density
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 161 - 172
Copyright
Copyright © Canadian Mathematical Society 2013

References

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